The son of Iconix Brand Group founder Neil Cole and nephew of designer Kenneth Cole got into an expletive-filled argument with two women outside the Boat Basin on the Upper West Side on Tuesday night that left one of the women with a swollen face.

A source involved told us Brandon Cole, 27, who works in business development for his father’s $1.7 billion Iconix, which owns brands Candie’s, the Sharper Image and Madonna’s Truth or Dare and Material Girl lines, was walking with a male friend near the West 79th Street Boat Basin, where a Saveur party was taking place.

According to the source, when Cole, who appeared inebriated, and his pal approached the ladies, one of them spoke with a Southern accent, prompting Cole to poke fun at her. He allegedly said to her, “Look at that Arkansas donk on you!” referring to her backside.

When the women tried to leave by hailing a taxi, our source said, Cole smacked the arm of one of them. The two then tangled arms as the woman was getting into the back seat.

As related by our source, Cole squeezed into the cab’s back seat next to the woman, while his male friend got in on the other side and the second woman hopped into the front. The three in the back seat tussled briefly before the guys finally jumped out, the source said.

An enraged Cole allegedly yelled, “You [bleeping] white-trash [bleep]! You need to back off, bitch. You’re in my city. You’re a visitor in my city! Now you can pay for my [bleeping] cab, [bleep]!”

A friend of his then e-mailed us to say that Cole and another witness both “vehemently deny these accusations” and that “Brandon never touched this woman. She jumped into his cab and sandwiched herself between Brandon and his friend. Both parties exchanged foul language, although they did share the cab across town.”